Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group GF of F . We determine the structure of the cohomology group H(U, Fp) as an Fp[GF /U ]-module for all n ∈ N. Previously this structure was known only for n = 1, and until recently the structure even of H(U, Fp) was determined only for F a local field, a case se...

The well-known notion of crossed module of groups is raised in this paper to the categorical level supported by the theory of categorical groups. We construct the cokernel of a categorical crossed module and we establish the universal property of this categorical group. We also prove a suitable 2-dimensional version of the kernelcokernel lemma for a diagram of categorical crossed modules. We th...

Let G be the Klein four-group and let k an arbitrary field of characteristic 2. A classification indecomposable kG-modules is known. We calculate relative cohomology groups Hχi(G,N) for every kG-module N, where χ set proper subgroups in G. This extends work Pamuk Yalcin to with non-trivial coefficients. also show that all cup products strictly positive degree Hχ*(G,k) are trivial.

This article studies the Albanese kernel TF (E × E), for an elliptic curve E over a p-adic field F . The main result furnishes information, for any odd prime p, about the kernel and image of the Galois symbol map from TF (E ×E)/p to the Galois cohomology group H(F, E[p] ⊗ E[p]), for E/F ordinary, without requiring that the ptorsion points are F -rational, or even that the Galois module E[p] is ...

We study the ring of differential operators D(X) on the basic affine space X = G/U of a complex semisimple group G with maximal unipo-tent subgroup U. One of the main results shows that the cohomology group H * (X, O X) decomposes as a finite direct sum of non-isomorphic simple D(X)-modules, each of which is isomorphic to a twist of O(X) by an automorphism of D(X). We also use D(X) to study the...

We study the ring of differential operators D(X) on the basic affine space X = G/U of a complex semisimple group G with maximal unipotent subgroup U . One of the main results shows that the cohomology group H(X,OX) decomposes as a finite direct sum of non-isomorphic simple D(X)modules, each of which is isomorphic to a twist of O(X) by an automorphism of D(X). We also use D(X) to study the prope...

We define an equivariant K0-theory for Yetter-Drinfeld algebras over a Hopf algebra with an invertible antipode. We show that there exists a pairing, generalizing Connes’ pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory.

We present various approaches to J. Herzog's theory of generalized local cohomology and explore its main aspects, e.g., (non-)vanishing results as well a general duality theorem which extends, much broader class rings, previous by Herzog-Zamani Suzuki. As an application, we establish prescribed upper bound for the projective dimension module satisfying suitable cohomological conditions, derive ...

Let A be a differential graded algebra with cohomology ring HA. A graded module over HA is called realisable if it is (up to direct summands) of the form HM for some differential graded A-module M . Benson, Krause and Schwede have stated a local and a global obstruction for realisability. The global obstruction is given by the Hochschild class determined by the secondary multiplication of the A...